JP6538084B2 - Phase matching system for multiple laser sources - Google Patents

Description

  The field of the invention relates to the field of coherent combining of a large number of elementary laser light sources.

  The coherent combination of laser light sources is particularly applicable to the generation of high energy laser light sources, for example with pulse widths of less than picoseconds, in the case of high power laser light sources and / or ultrashort pulse light sources.

  Acquisition of high power (or high energy) and high intensity laser light sources is currently constrained due to the instability of the gain material. One solution to this problem is to distribute the amplification in parallel across multiple gain media. To this end, it is necessary that the laser beams output from each gain medium be in phase to ensure all optimal coherent combination of the laser beams. Therefore, it is necessary to dynamically compensate for the induced delay across multiple or M laser beams due to propagation through an assembly of gain media (e.g., fiber amplifiers) connected in parallel. When phase-locked, the M initial laser beams interfere constructively, so the luminance is better than that of the basic amplifier, while maintaining the quality of the beam (eg, limited by diffraction for single mode fiber) Also forms a light source M times higher. Therefore, it is an issue to set the same number of phase locked loops as the emitters.

The architecture for phasing laser sources can be classified according to multiple criteria. First, there is a method of spatially combining or overlapping beams, and the following two types are distinguished.
-Tiled aperture connection. M laser beams are collimated and have parallel propagation directions. This coupled mode is the optical equivalent of a radar beamforming antenna. The tiled openings then have strong main lobes and parasitic side lobes.
-Full aperture connection. M beams are superimposed in the near field using polarizers or diffractive optical elements (DOE). In the case of the solid-aperture coupling method, efficiency is an advantage since there are no side lobes in the far field.

These include the nature of the error signal, and a process that allows the error signal to be countered over the phase between multiple laser sources and to optimize the coherent addition of the laser sources. Basically, four methods of coherently combining laser beams are distinguished and classified according to the amount of information contained in the negative feedback signal.
-A method called the "hill climbing" method. That is, the error signal is formed simply by excluding some of the coupled energy that is maximized by changing the phase of the M channels (beams) to be combined. This technique is based on a gradient based optimization algorithm in the M-1 dimension. The complexity in this example lies in the processing algorithm, and the error signal, which is a scalar signal, is extremely simple and inexpensive. The disadvantage of this method is the bandwidth of the loop changing by 1 / M. This method is therefore directed to a small number of coupled beams, typically less than ten.
-The method from the acronym of "optical heterodyne detection" to the OHD method. In this method, the error signal, which is a measurement of the phase of each emitter with respect to the reference beam, is a vector signal and one detector is used per channel. M measurements are taken in parallel via heterodyne mixing and demodulation. The disadvantages of this method are as follows.
○ Use RF elements that increase the cost per channel.
○ It depends on the reference beam.
O The error signal is measured prior to coupling, does not guarantee optimal coupling quality, and does not make it possible to compensate for in-phase fluctuations between the phase measurement plane and the coupling plane. Therefore, it is necessary to adjust the system.
-A method called LOCSET or synchronous multi-dither method. Similar to the hill-climbing method, this method uses a fraction of the binding energy as an error signal, but in this case contributions from the various channels are identified by "frequency marking" each channel via RF modulation. . The error signal for each beam is then obtained from heterodyne mixing using a reference beam. This method is advantageous because it requires only a single detector and that a high speed phase modulator can be used to recognize multiple channels. On the other hand, the need for multiple RF elements in the negative feedback loop (mixer, modulator, etc.) significantly increases the cost per channel of the system. Similar signals are obtained in this example by sequentially modulating each beam in time at the same frequency, which adversely affects the bandwidth of the system.
-A method of directly measuring the phase between the emitters, wherein the error signal is a map of the phases extracted from interferograms of the combined target beams that interfere with one another or with the reference beam. This direct interference measurement is comprehensive. That is, all phases are obtained through the recording of a single image by the matrix sensor and are therefore completely useful for a large number of emitters. The cost of the imager used is not critical as it is divided by the number of channels. On the other hand, the bandwidth of the system may be constrained by the sensors used, especially in the infrared. However, this is not a basic limitation. Finally, the phase is measured before bonding in the OHD method. That is, it is not possible to compensate for fluctuations such that the phase measurement plane and the coupling plane are in phase, so that an optimum coupling quality is not guaranteed. Therefore, calibration of the system is required.

  The following table summarizes the coherent combining techniques in the prior art. The shaded cells show the disadvantages of each method.

  Thus, a laser that simultaneously meets the requirement that the loop bandwidth be greater than 1 kHz, the number of beams potentially be 100, 1000 or more and that it operates at low cost without calibration (error signal in the coupling plane) Existing architectures that coherently combine beams do not exist at this time.

  The subject matter of the present invention is a system for spatially combining laser beams using diffractive optical elements (DOE). The system according to the invention is based on the inventive use of this diffractive element, and in addition to spatially combining the beams, it can generate an innovative error signal that makes it possible to compensate for the phase difference between the laser light sources. Make it This error signal is calculated from the intensity diffracted by the higher order diffractive coupler. Such an error signal can satisfy all the conditions described above.

More specifically, the subject matter of the present invention phase-matches M laser light sources of the same wavelength centered on λ ₀ (where M is an integer greater than 2) having a periodic spatial configuration. A system that
Means for collimating the M beams originating from the light source and for guiding them at different angles of incidence to the combined diffractive optical element with periodic phase gratings, these angles of incidence being equal to the period of the grating Means determined accordingly,
And-means for controlling the phase of the light source based on the negative feedback signal resulting from the combined beam.

This system is
-Means for excluding part of the combined beam,
A Fourier lens having an object plane and an image plane on this part path of the combined beam, the combined diffractive optical element being in its object plane,
A matrix of detectors in the image plane of the Fourier lens, which is capable of detecting the intensity distribution of part of the combined beam,
And-means for calculating a negative feedback signal based on these intensity distributions.

  A vector error signal (whose size is given by the number of higher order diffractions measured) is actually obtained, but it is not necessary to use an RF element. Furthermore, the system is in principle because the optimization is not directly phase-locked (see OHD and direct interference measurement techniques), but rather directly targets the coupling strength (by minimizing the higher order strength). Need not be calibrated.

Thus, the following set of advantages is obtained:
For the LOCSET and hill-climbing methods, the error signal occurs in the coupling plane and thus does not require calibration.
Since the error signal consists of a set of non-redundant measurements, it is possible to generate a negative feedback signal through simple processing operations.
The system cost per channel (beam) is relatively low, as the system does not contain any RF elements and only one detector per channel.
The system is compatible with a large number of channels and bandwidths exceeding 1 kHz.

  According to a feature of the invention, the means for calculating the negative feedback signal is defined by the coefficients obtained by expanding the phase of the combined diffractive optical element obtained over one period into a Fourier series, where M is an odd number Calculate the product of the intensity distribution detected in the plane of the detector matrix by the inverse matrix of size (2M-1) × (2M-1) if M and 2M × 2M if M is even Including means.

  Typically, M> 100.

  Preferably, the light sources are arranged in a one or two dimensional spatial arrangement.

  According to a preferred embodiment of the invention, the beams emanating from the laser light source have identical exit faces, and the system also comprises an objective face on which the exit face of the laser light source is located, and a combined diffractive optical element And includes another Fourier lens having an image plane.

  Other features and advantages of the present invention will become apparent on reading the following detailed description which is given by way of non-limiting example and with reference to the attached drawings.

The use of a diffractive optical element as a means of combining beams "from M to one" (five to one in the example of this figure) is schematically illustrated. 1 schematically illustrates an exemplary phase matching system according to the present invention. 1 schematically shows the intensity profile of a diffractive optical element used as a 1 to M (1 to 5 in this example) beam splitter. In a state in which the intensity distribution is diffracted by the diffractive optical element, the intensity profile of the diffractive optical element used as a means for coupling the beams from M to 1 (five to one in the example in this example) Show.

  The same reference numerals are assigned to the same elements in one figure.

  The gist of the invention is, first of all, a system based on the use of a diffractive optical element 1 (or DOE) as a means of combining various laser beams 10, as shown in the example of FIG. The laser beam 10 is incident on the DOE 1 at an angle defined by the spatial period of the DOE. If the beams are phase locked and have an optimal phase distribution (set by DOE), all beams constructively interfere at DOE 11 b order 0 (= main order) and break at higher order 11 a Interfere with each other.

  The principle of the present invention is to use the higher order DOE diffracted intensity distribution 11a as the error signal to optimize the coupling, as shown in the example of FIG. In the scheme of the present application, with respect to the LOCSET and hill climbing techniques, the error signal is measured at the end of the chain (ie after DOE), so all of the interference experienced by the beam can be taken into account. Note that if the example of FIG. 2 shows a laser beam linear array, and thus a one-dimensional DOE, the proposed solution still applies equally to a two-dimensional array of laser beams and a two-dimensional DOE.

A system for phase-matching M laser light sources according to the present invention will be described with reference to FIG. The M laser light sources have the same wavelength centered at λ ₀ . These laser light sources may be pulsed light sources. The pulse width may also be less than ^10-12 seconds.

The system includes:
M phase modulators, ie one modulator 4 at the output of each laser source.
Combined DOE 1 with a phase grating of predetermined spatial period located in the image plane of the Fourier lens 14. The M beams emanating from the modulator are directed by this Fourier lens 14 to DOE 1. Each beam is incident on the DOE at a particular angle of incidence defined by the DOE's spatial period.
A means for excluding a portion 12 of the combined beam 11, such as a high reflection mirror 5 (for example excluding 1%) or a polarizing cube beam splitter. Preferably, it is selected to exclude less than 1 / M. Another part of the combined beam forms the output beam 13 of the system.
A second Fourier lens 6 in the object plane in which the integrated DOE 1 is located.
A matrix of detectors 7 in the image plane (= plane B) of the second Fourier lens 6, which is capable of detecting the fractional intensity distribution 11b, 11a of the diffraction orders of the beams combined by DOE1.
Means 8 for calculating a negative feedback signal from these distributions in the plane of the matrix of detectors. These calculation means 8 are connected to them to control the M phase modulators 4.

The M beams can be directed to DOE1 in various ways. The system upstream of the DOE, eg
-An identical master oscillator 2 connected to the "1 to M" coupler 3 to generate M laser light sources,
Potentially including M amplifiers 9 each connected to a phase modulator 4;

  The exit surface (= plane A) of the M laser beams (from the amplifier or modulator) is located in the object plane of the Fourier lens 14 in a spatially periodic arrangement of pitch P shown in FIG.

  According to a variant, the M laser light sources have a collimator lens associated with each light source and are periodic such that the beams are incident on the combined DOE at a specific incident angle defined by the spatial period of the DOE It is directly arranged in various angles and spatial configurations.

The means 8 for calculating the negative feedback signal are considered below. The problems to be solved by these calculation means are therefore raised as follows.
The variable in question is the spatial distribution of the electromagnetic field formed from the superposition of the electromagnetic fields originating from each laser light source.
It is assumed that the intensity distribution of the electromagnetic field is known to lie in two separate planes. That is, a uniform (or measured) distribution I _A in the exit face of the light source (plane A in FIG. 2) and a distribution I _B measured after being coupled by DOE (in plane B in FIG. 2) It is.

が

となるように平面ＡおよびＢ内での位相φ_Ａおよびφ_Ｂの分布を計算することである。 Its purpose is to digitally propagate the electromagnetic field from A to B

But

The distribution of the phases φ _A and φ _B in planes A and B is calculated so that

  This problem is similar, for example, to the problem in the measurement of the phase deviation from the intensity image distortions encountered in astronomy. An exemplary way of solving this problem can be found in the literature. The following documents can be cited: That is, R. G. Paxman and J. R. Fienup, “Optical misalignment sensing and image reconstruction using phase diversity”, J. Opt. Soc. Am. A 5, 914-923 (1988), or J.A. N. Cederquist, J.M. R. Fienup, C.I. C. Wackerman, S .; R. Robinson, and D. Kryskowski, "Wave-front phase estimation from Fourier intensity measurements", J. Org. Opt, Soc. Am A6, 1020-1026 (1989), or R.A. G. Paxman, T .; J. , Schulz, J. et al. R. Fienup, "Joint estimation of object and aberrations by using phase diversity", J.F. Opt. Soc. Am, A9, 1072-1085 (1992).

  The main disadvantage of this type of method is that it takes a potentially long computation time (typically more than one second) to use the digital Fourier transform (for calculations involving light propagation from A to B to solve) Also much longer).

  In the system according to the invention, the significant simplification of the phase calculation is due to the fact that the calculation of the field distribution of plane B from the field distribution of plane A can be done by a simple product using a known matrix.

であり、またはＭ＝２Ｎであれば、

であり、さもなければ、

であり、ここで、
− ωは平面Ａ内のビーム（ガウシアンと仮定される）のウエストであり、
− Ｐは平面Ａ内のビームの位置の周期であり、
− α_ｋは第ｋビームの振幅に関する重み係数（本例では例えばα_ｋ＝１、但しＭ＝２Ｎ＋１であればｋは−Ｎ〜＋Ｎであり、Ｍ＝２Ｎであればｋは−Ｎ＋１〜＋Ｎであり、さもなければα_ｋ＝０）であり、
− φ_ｋは第ｋビームの光位相であり、
− δはディラック関数、および＊は重畳演算子である。 Specifically, for M laser beams considered in A, the electric field distribution of A can be written according to the parity of M as follows.
If M = 2N + 1, then

Or if M = 2N

Otherwise,

And here
-Ω is the waist of the beam in plane A (assumed to be Gaussian),
-P is the period of the position of the beam in plane A,
− Α _k is a weighting coefficient relating to the amplitude of the k-th beam (in this example, for example, α _k = 1, where k is −N to + N if M = 2N + 1, and k is −N + 1 to + N if M = 2N Otherwise α _k = 0),
− Φ _k is the optical phase of the k th beam,
-Δ is the Dirac function, and * is the convolution operator.

The electric field in the plane of the DOE is obtained by the Fourier transform of E _A (x ⁾ and multiplication with the transfer function ^{eiφDOE (u)} on the phase of the DOE.

The electric field propagated to the measurement plane (plane B) is obtained again via the Fourier transform of E _DOE (u).

従って、

である。 Furthermore, similar to the phase of the DOE, the structure makes it possible to write the periodic function e ^{iφDOE (u)} with a period of 1 / P (think u in the far field ⁾ in Fourier series form.

Therefore,

It is.

A combined DOE is calculated to combine M beams into one. In contrast, one beam diffracted by the same DOE essentially has M beams of the same order (主 I ₁ ) of the same intensity (referred to as the main beam) and a smaller intensity I ₂ (I ₂ <<I ₁ ) Generate an infinite number of beams of higher orders. In other words, this means the following relationship for the coefficient _ck :
| C _k | ² 1/1 / M (k is −N to + N when M = 2N + 1, and k is −N + 1 to + N when M = 2N)
| C _k | ² << 1 / M (other than the above)

The term c _{k + h} α _h of the above equation for E _B (x) is therefore
[−N ≦ k + h ≦ + N] ∪ [−N ≦ h ≦ + N] (when M = 2N + 1), or [−N + 1 ≦ k + h ≦ + N] ∪ [−N + 1 ≦ h ≦ + N] (M = 2N If)
Has an unignorable value of. Or
k ∈ {-2 N, ..., + 2 N} (when M = 2 N + 1), or k ∈ {-2 N + 1, ..., + 2 N} (when M = 2 N)
It is.

またはＭ＝２Ｎの場合に−２Ｎ＋１から＋２Ｎとなる：

場合に正確であると考えられる。 In general, the equation for E _B (x) is thus from −2N to + 2N when the indices k and h are M = 2N + 1:

Or -2N + 1 to + 2N for M = 2N:

It is considered to be accurate.

ここで、Ｅ_Ａ，ｋ（およびＥ_Ｂ，ｋ）は電場Ｅ_Ａ（ｘ）（およびＥ_Ｂ（ｘ））の複素重み係数であり、ｘ＝ｋＰの近傍では、

である。 The matrix product equation is then identified and can be written as follows for M = 2N + 1:

Where E _{A, k} (and E _{B, k} ) is the complex weighting factor of the electric field E _A (x) (and E _B (x)), and in the vicinity of x = _{k P}

It is.

H _DOE is a matrix defined by expansion coefficients c _k to Fourier series of the phase of DOE taken over one period. This matrix is thus known a priori through the construction of the DOE. As mentioned above, in practice, DOE is calculated to combine M laser beams when the odd M is equal to 2N + 1, so 2 M -1 Fourier series to obtain the following equation The coefficient of is required.

次数−２Ｎ〜＋２Ｎの回折された次数（平面Ｂ内のｘ＝ｋＰの近傍、ｋ∈｛−２Ｎ，・・・，２Ｎ｝）のみが計算にとって重大な強度を有しているという事実を考慮して、Ｍ＝２Ｎ＋１の場合における２Ｍ−１個の係数の非限定的な選択も図３ａおよび３ｂに示す。 If M is an even number equal to 2N, then 2M coefficients are required.

Taking into account the fact that only diffracted orders of the order -2N to + 2N (near to x = kP in plane B, k ∈ {-2N, ..., 2N}) have significant strength for the calculation Thus, non-limiting selection of 2M-1 coefficients in the case of M = 2N + 1 is also shown in FIGS. 3a and 3b.

The light propagation of M beams from plane A to plane B is thus a matrix of size (2M-1) × (2M-1) if M is odd and a 2M × 2M matrix if M is even Calculated through a simple product of (matrix H _DOE ) and vector E _A. The Fourier transform used in the usual way is _replaced by this matrix H _DOE . Thus, the calculation of the electromagnetic field distribution in plane A from the distribution detected in plane B by the matrix of photodetectors is simply the inverse of this matrix H _DOE and the intensity distribution detected in plane B. It is realized through multiplication.

From the electromagnetic field distribution thus calculated in plane A, the phase is calculated as before. Such a simplified calculation of the electromagnetic field distribution in plane A significantly improves, for example, the speed of the phase calculation algorithm (= calculation of the negative feedback signal) which is iterative or searching for the largest kind, These means of calculating the negative feedback signal can be implemented in real time, even for several thousand beams. The calculations described in the following document can be cited as an exemplary iterative phase calculation.
-J. Markham and J. A. Conchello, "Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur", J. Am. Opt. Soc. Am. A 16 (10), 2377-2391 (1999);
-J. R. Fienup, "Phase retrieval algorithms: a comparison", Appl. Opt. 21 (15), 2758-2769 (1982).

  In the above example, the coupled DOE works by transmission, but the system of the invention is also effective when using a reflective DOE.

Claims (7)

A system for phase matching M (where M is an integer greater than 2) laser light sources of the same wavelength centered on λ ₀ , having a periodic spatial configuration,
-Means for collimating M beams originating from the light source and guiding the beams to the combined diffractive optical element (1) having a periodic phase grating at different incident angles θ _2k , said incident angles Means determined according to the period of the grid,
Means for controlling the phase of the light source based on a negative feedback signal resulting from the combined beam;
-Means (5) for excluding a portion (12) of the combined beam;
A Fourier lens (6) having an object plane and an image plane on the path of the part of the combined beam, wherein the combined diffractive optical element (1) is in its object plane and ,
A matrix (7) of detectors (7) in the image plane of the Fourier lens (6), which is capable of detecting the intensity distribution of the part of the combined beam , In the system,
-Means (8) for calculating the negative feedback signal based on the intensity distribution, said means (8) obtained by expanding the phase of the combined diffractive optical element obtained over one period into a Fourier series The plane of the matrix of said detector by the inverse matrix of size (2M-1) × (2M-1) if M is odd and 2M × 2M if M is even, as defined by the coefficients A system, characterized in that it comprises means for calculating the product of the intensity distribution detected therein.   The system of claim 1, wherein said laser source is pulsed. A system as claimed in claim 1 or 2, characterized in that the pulse width is less than ^10-12 seconds.   A system as claimed in any one of the preceding claims, characterized in that M> 100.   5. A system as claimed in any one of the preceding claims, characterized in that the excluded part is less than 1 / M.   A system as claimed in any one of the preceding claims, wherein the light sources are arranged in a one or two dimensional spatial arrangement.   The beams originating from the laser light source have the same exit surface, and the system comprises an objective surface on which the exit surface of the laser light source is located, and an image surface on which the combined diffractive optical element (1) is located. A system as claimed in any one of the preceding claims, characterized in that it comprises another Fourier lens (14).

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